There is a growing literature on learning in the context of individualized treatment rules that map an individual's observable characteristics to a treatment. See [1]}, [2]}, [3]}, [4]}, [5]}, and [6]}, among others. Our analysis does not incorporate individuals' observable covariates. Since the nonlinear regret risk aggregates the conditional nonlinear regret risk additively, it is straightforward to incorporate observable discrete covariates into our analysis, i.e., an optimal individualized fractional assignment rule that applies an optimal fractional assignment rule to each subpopulation of individuals sharing the same covariate value.
